Solve 4x*5x=32

$$4x \times 5x=32$$

Solve for x

$$x = \frac{2 \sqrt{10}}{5} \approx 1.264911064$$

$$x = -\frac{2 \sqrt{10}}{5} \approx -1.264911064$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$4x^{2}\times 5=32$$

Multiply 4 and 5 to get 20.

$$20x^{2}=32$$

Divide both sides by 20.

$$x^{2}=\frac{32}{20}$$

Reduce the fraction \frac{32}{20} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{8}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{10}}{5} x=-\frac{2\sqrt{10}}{5}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$4x^{2}\times 5=32$$

Multiply 4 and 5 to get 20.

$$20x^{2}=32$$

Subtract 32 from both sides.

$$20x^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20\left(-32\right)}}{2\times 20}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20\left(-32\right)}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80\left(-32\right)}}{2\times 20}$$

Multiply -80 times -32.

$$x=\frac{0±\sqrt{2560}}{2\times 20}$$

Take the square root of 2560.

$$x=\frac{0±16\sqrt{10}}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±16\sqrt{10}}{40}$$

Now solve the equation x=\frac{0±16\sqrt{10}}{40} when ± is plus.

$$x=\frac{2\sqrt{10}}{5}$$

Now solve the equation x=\frac{0±16\sqrt{10}}{40} when ± is minus.

$$x=-\frac{2\sqrt{10}}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{10}}{5} x=-\frac{2\sqrt{10}}{5}$$